For some intuition we refer the reader to fig:lit. The above complexity measure appears in the definition of the multiclass Littlestone dimension [1]}. In fact, a class \(\mathcal {H}\subseteq [k]^\mathcal {X}\) 
has multiclass Littlestone dimension \(d\)  if it has a multiclass Littlestone tree of depth \(d\)  but not of depth \(d+1\) . We underline that having an infinite multiclass Littlestone tree is not the same as having an unbounded multiclass Littlestone dimension. A class
\(\mathcal {H}\)  has unbounded Littlestone dimension if for
every \(d \in \mathbb {N}\)  there is some tree of depth \(d\) .
However, this does not mean that there is a single
infinite tree. This is a fundamental conceptual gap between the uniform and the universal settings.
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